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E φ E φ
F={(x, y, z)∈R3, x −y+ 3z= 0}G={(x, y, z)∈R3, y −z= 2x+z= 0}F G
R3F G
u v u0= 1 v0= 2 n∈Nun+1 = 3un+ 2vnvn+1 = 2un+ 3vn
u−v
u
u v n +∞
f f(x) = 
0x= 0
x
ln(x)
D f
f
fC1[0; 1[
f f(e)
v v0= 3 n∈Nvn+1 =vn
ln(vn)
∀n∈N, vn≥e
v
∀x≥e, 0≤f0(x)≤1
4
∀n∈N,|vn−e| ≤ 1
4n
45>1000 n1vne10−12
EKφ∈ L(E)p∈N
Np=Ker(φp)Ip=Im(φp)
φ0=IdEk∈N∗φk=φ◦φk−1φ φ2=φ
N0I0
p∈NNpIpE
p≥1N0⊂N1⊂N2⊂... ⊂Np−1⊂Np
p≥1Ip⊂Ip−1⊂... ⊂I1⊂I0
E n
p∈NdimIp+dimNp=n
N1=N2⇔I1=I2
N1I1E
N1I1E
r r ≤n Nr=Nr+1
r
Ir=Ir+1
p∈NNr=Nr+pIr=Irp
NrIrE